For stochastic control problems with partial information, there has been considerable literatures about forward-backward stochastic controlled systems. Wang and Wu [1]} obtained a global maximum principle for partially observed stochastic recursive optimal control problem, under the assumption that control domain is not necessarily convex and the forward diffusion coefficient does not contain control variable. Wu [2]} studied a partially observed stochastic control problem of FBSDEs and a local maximum principle was proved. Shi and Wu [3]} obtained a partially observed maximum principle of controlled fully coupled FBSDEs on the assumption that the forward diffusion coefficient does not contain the control variable and the control domain is not necessarily convex. Wang et al. [4]} studied a partial observed stochastic control problem of FBSDEs with correlated noises between the system and the observation. Three versions of maximum principle were established by using a direct method, an approximation method and a Malliavin derivative method, respectively. By introducing a state decomposition and backward separation approach, Wang et al. [5]} studied an linear-quadratic (LQ for short) stochastic control problem of FBSDEs, where the drift coefficient of the observation equation is linear with respect to state \(x\) , and the observation noise is correlated with the state noise. Some recent progress for partially observed problems, has been made in mean-field type controls (see [6]}, [7]}, [8]}), differential games (see [9]}, [10]}, [11]}, [12]}, [13]}), random jumps (see [14]}, [15]}, [16]}, [17]}, [18]}, [19]}), time delay (see [20]}) and applications in finance (see [21]}, [22]}). The partially observed stochastic control problem is usually associated with the state filtering and estimation technique, and we only list some main references such as [23]}, [24]}, [25]}, [26]}, [18]}, [28]}, [29]}.
